Database management systems (DBMSs) are notoriously difficult to deploy and administer. The goal of a self-driving DBMS is to remove these impediments by managing itself automatically. However, a critical problem in achieving full autonomy is how to predict the DBMS's runtime behavior and resource consumption. These predictions guide a self-driving DBMS's decision-making components to tune and optimize all aspects of the system. We present the ModelBot2 end-to-end framework for constructing and maintaining prediction models using machine learning (ML) in self-driving DBMSs. Our approach decomposes a DBMS's architecture into fine-grained operating units that make it easier to estimate the system's behavior for configurations that it has never seen before. ModelBot2 then provides an offline execution environment to exercise the system to produce the training data used to train its models. We integrated ModelBot2 in an in-memory DBMS and measured its ability to predict its performance for OLTP and OLAP workloads running in dynamic environments. We also compare ModelBot2 against state-of-the-art ML models and show that our models are up to 25x more accurate in multiple scenarios.